Question

Check whether (x+3) is a factor of 2x³ + 2x²+ 4x+7

Answer 1

Answer:

x+3 is the factor of the polynomial

Answer 2

Answer:

No it is not a factor of the polynomial

Step-by-step explanation:

Here we have been given an expression which is as below;

$2x^{3} + 2x^{2} + 4x + 7$

We have to check whether x + 3 is a factor of the given expression or not.

For this we assume,

g(x) = x +3

Let g(x) = 0

∴ x + 3 = 0

⇒ x = -3

We get, x = -3 and we put it in the expression above if the remainder comes to be zero then g(x) will be the respective factor of the given expression.

Putting x = -3

∴ $2(-3)^{3} + 2 (-3)^{2} + 4 (-3) + 7$

= 2 × (-27) + 2 × 9 - 12 +7

= -54 + 18 -12+7

= 18 +7 -54 - 12

= 25 - 66

= -41

Now as we can see that the remainder is not zero hence x+ 3 is not a factor of this polynomial.